A local sensitivity analysis for the hydrodynamic Cucker-Smale model with random inputs

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Ha, Seung Yeal^1,2,3  Jin, Shi^4,5  Jung, Jinwook¹  Shim, Woojoo¹ 

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[3] Korea Inst Adv Study, Hoegiro 87, Seoul 02455, South Korea

[4] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China

[5] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai 200240, Peoples R China

关键词: Cucker-Smale model;    Flocking;    Hydrodynamic limit;    Local sensitivity analysis;    Random communication;    Uncertainty quantification;   

DOI  :  10.1016/j.jde.2019.08.031

来源: Elsevier

【 摘 要 】

We present a local sensitivity analysis for the hydrodynamic Cucker-Smale (HCS) model with random inputs. In the absence of random inputs, the HCS model was derived as a macroscopic model for the emergent dynamics of the CS flocking ensemble from the kinetic CS model via the moment method and mono-kinetic ansatz for a closure condition. In this paper, we incorporate the uncertain effects together with the HCS model to result in the random HCS model. For definiteness, we consider the uncertainties in initial data and communication weight function. For this random HCS model, we perform local sensitivity estimates such as the propagation of pathwise well-posedness, pathwise L-2-stability and flocking estimates of solution process. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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